Let be a domain with Lipschitzian boundary of a compact Riemannian manifold (M,g) and p>1. We prove that we can make the volume of M arbitrarily close to the volume of while the first eigenvalue of the p-Laplacian on M remains uniformly bounded from below in terms of the the first eigenvalue of the Neumann problem for the p-Laplacian on .
Soit un domaine à bord Lipschitz d'une variété riemannienne compacte (M,g) et p>1. Nous montrons qu'on peut rendre le volume de M arbitrairement proche du volume de tout en gardant la première valeur propre du p-Laplacien sur M uniformement minorée en termes de la première valeur propre du problème de Neumann pour le p-Laplacien sur .
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Ana-Maria Matei 1
@article{CRMATH_2002__335_3_255_0, author = {Ana-Maria Matei}, title = {The effect of perturbations on the first eigenvalue of the $ \mathbf{p}${-Laplacian}}, journal = {Comptes Rendus. Math\'ematique}, pages = {255--258}, publisher = {Elsevier}, volume = {335}, number = {3}, year = {2002}, doi = {10.1016/S1631-073X(02)02464-0}, language = {en}, }
Ana-Maria Matei. The effect of perturbations on the first eigenvalue of the $ \mathbf{p}$-Laplacian. Comptes Rendus. Mathématique, Volume 335 (2002) no. 3, pp. 255-258. doi : 10.1016/S1631-073X(02)02464-0. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02464-0/
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